A new kind of representations on noncommutative phase space
arXiv:0902.3782 · doi:10.1016/j.physleta.2008.10.052
Abstract
We introduce new representations to formulate quantum mechanics on noncommutative phase space, in which both coordinate-coordinate and momentum-momentum are noncommutative. These representations explicitly display entanglement properties between degrees of freedom of different coordinate and momentum components. To show their potential applications, we derive explicit expressions of Wigner function and Wigner operator in the new representations, as well as solve exactly a two-dimensional harmonic oscillator on the noncommutative phase plane with both kinetic coupling and elastic coupling.
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Cited by in corpus (4)
- Induced entanglement entropy of harmonic oscillators in noncommutative phase space
- Some Biorthogonal Families of Polynomials Arising in Noncommutative Quantum Mechanics
- Connes spectral distance and nonlocality of generalized noncommutative phase spaces
- Connes distance of harmonic oscillators in quantum phase space